Edexcel 2020 Pure Maths Paper 2 Question Paper (pdf)
Edexcel 2020 Pure Maths Paper 2 Mark Scheme (pdf)
- The table below shows corresponding values of x and y for y =
The values of y are given to 4 significant figures.
(a) Use the trapezium rule, with all the values of y in the table, to find an estimate for
giving your answer to 3 significant figures.
- Relative to a fixed origin, points P, Q and R have position vectors p, q and r respectively.
- P, Q and R lie on a straight line
- Q lies one third of the way from P to R
show that q = 1/3(r + 2p)
- (a) Given that
2log (4 − x) = log(x + 8)
x2 − 9x + 8 = 0
(b) (i) Write down the roots of the equation
x2 − 9x + 8 = 0
(ii) State which of the roots in (b)(i) is not a solution of
2log(4 − x) = log(x + 8)
giving a reason for your answer.
- In the binomial expansion of
(a + 2x)7
where a is a constant
the coefficient of x4 is 15 120
Find the value of a.
- The curve with equation y = 3 × 2x
meets the curve with equation y = 15 − 2x+1 at the point P.
Find, using algebra, the exact x coordinate of P.
- (a) Given that
find the values of the constants A, B and C
- Figure 1 shows a sketch of the curve C with equation
- A curve C has equation y = f(x)
- fʹ(x) = 6x2 + ax − 23 where a is a constant
- the y intercept of C is −12
- (x + 4) is a factor of f(x)
find, in simplest form, f(x)
- A quantity of ethanol was heated until it reached boiling point.
The temperature of the ethanol, θ °C, at time t seconds after heating began, is modelled
by the equation
θ = A − Be−0.07t
where A and B are positive constants.
- the initial temperature of the ethanol was 18°C
- after 10 seconds the temperature of the ethanol was 44°C
(a) find a complete equation for the model, giving the values of A and B
to 3 significant figures.
Ethanol has a boiling point of approximately 78°C
(b) Use this information to evaluate the model.
- (a) Show that
cos 3A ≡ 4cos3 A − 3 cosA
(b) Hence solve, for −90° x 180°, the equation
1 − cos3x = sin2 x
- Figure 2 shows a sketch of the graph with equation
y = 2 | x + 4| − 5
The vertex of the graph is at the point P, shown in Figure 2.
(a) Find the coordinates of P.
(b) Solve the equation
3x + 40 = 2 | x + 4| − 5
A line l has equation y = ax, where a is a constant.
Given that l intersects y = 2| x + 4| − 5 at least once,
(c) find the range of possible values of a, writing your answer in set notation.
- The curve shown in Figure 3 has parametric equations
x = 6sint y = 5 sin 2t 0 t π/2
The region R, shown shaded in Figure 3, is bounded by the curve and the x-axis.
- The function g is defined by
- A circle C with radius r
- lies only in the 1st quadrant
- touches the x-axis and touches the y-axis
The line l has equation 2x + y = 12
(a) Show that the x coordinates of the points of intersection of l with C satisfy
5x2 + (2r − 48) x + (r2 − 24r + 144) = 0
Given also that l is a tangent to C,
(b) find the two possible values of r, giving your answers as fully simplified surds.
- A geometric series has common ratio r and first term a.
Given r ≠ 1 and a ≠ 0
(a) prove that
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